Question: $g(x) = -3x^{2}-2x-7+4(f(x))$ $f(x) = -6x^{2}-2(h(x))$ $h(x) = -4x^{2}+3x$ $ h(f(2)) = {?} $
Explanation: First, let's solve for the value of the inner function, $f(2)$ . Then we'll know what to plug into the outer function. $f(2) = -6(2^{2})-2(h(2))$ To solve for the value of $f$ , we need to solve for the value of $h(2)$ $h(2) = -4(2^{2})+(3)(2)$ $h(2) = -10$ That means $f(2) = -6(2^{2})+(-2)(-10)$ $f(2) = -4$ Now we know that $f(2) = -4$ . Let's solve for $h(f(2))$ , which is $h(-4)$ $h(-4) = -4(-4)^{2}+(3)(-4)$ $h(-4) = -76$